Abstract

This paper deals with nonlinear modeling of planar one- and two-link, flexible manipulators with rotary joints using finite element method (FEM) based approaches. The equations of motion are derived taking into account the nonlinear strain-displacement relationship and two characteristic velocities, $U_a$ and $U_g$, representing material and geometric properties (also axial and flexural stiffness) respectively, are used to nondimensionalize the equations of motion. The effect of variation of $U_a$ and $U_g$ on the dynamics of a planar flexible manipulator is brought out using numerical simulations. It is shown that above a certain $U_g$ value (approximately \geq 45 m/s), a linear model (using a linear strain-displacement relationship) and the nonlinear model give approximately the same tip deflection. Likewise, it was found that the effect of $U_a$ is prominent only if $U_g$ is small. The natural frequencies are seen to be varying in a nonlinear manner with $U_a$ and in a linear manner with $U_g$.

Item Type:

Journal Article

Additional Information:

Copyright of this article belongs to American Society of Mechanical Engineers.